Fredholm determinants, differential equations and matrix models

Communications in Mathematical Physics

Volumn 163, Issue 1, 1994, Pages 33-72

  Tracy, Craig A ^a   Widom, Harold ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003025563     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/BF02101734     Document Type: Article

References (41)

1. Zero-field susceptibility of the two-dimensional Ising model near Tc
2. Asymptotics of level spacing distributions for random matrices
3. Integral equations and exact solutions for the fourth Painlevé transcendent
4. Estimates of asymmetric Freud polynomials
5. Estimates of the Hermite and the Freud polynomials
6. Universal scaling of the tail of the density of eigenvalues in random matrix models
7. Large N limit and discretized two-dimensional quantum gravity
8. Exactly solvable field theories of closed strings
9. Integral equations and connection formulae for the Painlevé equations
10. Strings in less than one dimension and the generalized KdV hierarchies
11. Strings in less than one dimension
12. Statistical theory of energy levels of complex systems, I, II, and III
13. Fredholm determinants and inverse scattering problems
14. The spectrum edge of random matrix ensembles
15. Nonperturbative two-dimensional quantum gravity
16. Differential equations for quantum correlation functions
17. Monodromy problem and the boundary condition for some Painlevé equations
18. Monodromy preserving deformations of linear ordinary differential equations with rational coefficients. II
19. Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
20. Painlevé functions of the third kind
21. Level spacing functions and nonlinear differential equations
22. A non-linear differential equation and a Fredholm determinant
23. Matrix models of 2D gravity and isomonodromic deformation
24. A new family of unitary random matrices
25. Correlation functions of random matrix ensembles related to classical orthogonal polynomials
26. Studies on the Painlevé equations II. Fifth Painlevé equation Pv. Japan
27. Studies on the Painlevé equations III. Second and Fourth Painlevé Equations, PII and PIV
28. Studies on the Painlevé equations IV. Third Painlevé equation PIII
29. Introduction to random matrices
30. Level-spacing distributions and the Airy kernel
31. Level-spacing distributions and the Bessel kernel
32. Spin-spin correlation functions of the two-dimensional Ising model: Exact theory in the scaling region